We address an optimization problem that arises at seaports where containers are transported between stacking areas and small buffer areas of restricted capacity that are located within the reach of quay cranes. The containers are transported by straddle carriers that have to be routed such that given unloading and loading sequences of the containers at the quay cranes are respected. The objective is to minimize the turnaround times of the vessels. We analyze the problem’s computational complexity, present an integer program, and propose a heuristic framework that is based on decomposing the problem into its routing component and a component that handles the time variables and buffer capacities. The framework is analyzed in computational tests that are based on real-world data. Based on these tests, we analyze the question of whether or not it pays off to deviate from the approach of permanently assigning a fixed number of straddle carriers to each quay crane, which is the strategy that is currently implemented at the port.

Introduction

A container port is a complex system consisting of berths equipped with quay cranes, transport vehicles, stacking areas, stacker cranes, and road or rail connections to the hinterland. Each container port is a unique combination of these components and features an individual vehicle fleet. Large ports handle several million twenty-foot equivalent units (TEU) on an annual basis. Port authorities therefore strive for sophisticated planning approaches based on simulation or optimization techniques in order to stay competitive. Operations research challenges at seaports are mostly concerned with problem settings that directly or indirectly affect the flow of containers within the ports. Container ports that can serve several vessels simultaneously aim at high berth utilization rates, so that decision makers have to determine appropriate assignments of vessels to berths. Each berth is equipped with one or multiple quay cranes. These cranes are needed for the process of loading and unloading containers and have to be scheduled appropriately. Inbound containers, i.e., containers that arrive by vessels, must then be transported to large stacking (or storage) areas, where they are temporarily stored for later processing by train, truck or vessel. Outbound containers, i.e., containers that arrive by train or truck and that have to be loaded onto a vessel, have to be transported in the reverse direction. The corresponding transportation requests within the seaport can be executed by different types of vehicles. Automated guided vehicles (AGVs) and manually driven yard trucks (YTs) cannot lift or drop containers. They have to be loaded and unloaded at predefined handover positions by quay cranes at the vessels or by yard cranes (or gantry cranes) at the storage areas. Automated lifting vehicles (ALVs) are able to perform lifting and dropping operations. However, yard cranes remain necessary for stacking operations.

This paper investigates a cooperative uplink system where two users wish to send messages to a base station with the help of a buffer-aided relay. Transmission modes in terms of both non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) are considered. For the considered system, the probability for the user-to-relay channels to successfully perform NOMA is first theoretically derived in two scenarios of dynamic and fixed power controls (PCs) at users. Then, an efficient buffer-aided hybrid NOMA/OMA based mode selection (MS) scheme is proposed, which adaptively switches between the NOMA and OMA transmission modes according to the instantaneous strength of wireless channels and the buffer state. The state transmission matrix probabilities of the corresponding Markov chain is also derived, and the performance of the proposed hybrid NOMA/OMA scheme is analyzed with closed-form expressions, in terms of sum throughput, outage probability, diversity gain, and average packet delay. For both the dynamic and fixed PCs, the proposed scheme is proved to achieve a diversity gain of two when the buffer size is not smaller than three, which means that fixed PC will not lead to a loss of diversity gain.

Introduction

Non-orthogonal multiple access (NOMA) technology, using successive interference cancellation (SIC) and multiplexing in power-domain, can improve spectrum efficiency, which is considered to be a promising fifth-generation mobile communication technology [1]. NOMA allows multiple users to share the communication resources simultaneously, i.e., time, frequency and code domain, then achieves better performance than conventional orthogonal multiple access (OMA) [2]–[4]. Cooperative communication can further enhance the efficiency and reliability, and expand the coverage of wireless communication networks. In order to enhance the performance of NOMA, the work in [5] first exploited cooperation between the users, i.e., the stronger users help the other weaker users by using the decode-and-forward (DF) scheme, so that the optimal diversity gain can be achieved. On the other hand, the work in [6], [7] investigated cooperative NOMA with a single relay, where multiple users were helped by a dedicated relay node using the DF and amplify-and-forward (AF) schemes. In addition, relay selection (RS) scheme has also been proposed for cooperative NOMA networks with multiple relays in some existing works (e.g., [8]–[11]). Recently, the uplink cooperative communication has also been investigated in [12], where a coordinated direct and relay transmission was proposed.